Abstract
We propose a method for obtaining a monotonically decreasing sequence of upper bounds of the percolation threshold of a Bernoulli random field on ℤ2. On the basis of this sequence, we develop a method for the construction of approximations with guaranteed exactness estimate for the percolation probability. The first term of the sequence is calculated (c 2 = 0.74683).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1315–1326, October, 2005.
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Virchenko, Y.P., Tolmacheva, Y.A. Majorant estimates for the percolation threshold of a Bernoulli field on a square lattice. Ukr Math J 57, 1535–1549 (2005). https://doi.org/10.1007/s11253-006-0012-x
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DOI: https://doi.org/10.1007/s11253-006-0012-x